Clock time differences

Suppose two highly precise, identical clocks are synchronized and one clock is placed on the North Pole and the other on the equator. After 310 years, how much will the clocks differ in time? Assume the Earth is a perfect sphere. Please show all work

Speed of Earth at the equator is

$ V =1670 km/h =1670000/3600 =463.88 m/s$

The time is becoming smaller for moving objects. (moving clocks run slowly)

$T0 = 310 years$

$T = T0*\sqrt{(1-V^2/c^2)} = 310*\sqrt(1-463.88^2/9*10^16) =$ $=309,99999999963080894444422460245 years=$

$=9776159999,9883128910502202142042 seconds$

Difference in time

$T0-T =0.0117 seconds$